Israel Folau emphasised his immense worth to Australian rugby by producing the million-dollar touches for a grinding 21-15 win over Scotland in a Murrayfield bog on Sunday morning (AEDT).

Folau combined brilliantly with Quade Cooper to score a try, helped set up another and saved two as the Wallabies put a tumultuous week behind them with the relieving two-tries-to-nil win.

Coach Ewen McKenzie predicted it would be a massive test of character and one of the side's greatest challenges after he stood down five players for the match for drinking last week in Dublin.

It turned out to be just that as the inspired Scots, with big lock Jim Hamilton showing the way in his 50th Test, pushed Australia throughout in front of an Edinburgh crowd of 57,630.

A rare off day with the boot by goal-kicker Christian Leali'ifano, who went just four for nine on the loose surface, made it even harder for the Wallabies and they only sealed the result thanks to the pack's ability to stop two late driving mauls near the line.

Hard-working skipper Ben Mowen then capped a fine game by forcing a breakdown penalty in the last minute with the home side hot on attack.

In all, Australia was forced to make almost twice as many tackles but its defence held firm to keep the goal-line intact.

The Wallabies looked in trouble when lock Rob Simmons was sin-binned for lashing out at Scottish prop Moray Low, niggling at the back of a ruck, in the 48th minute.

Greig Laidlaw then kicked his fifth penalty from six attempts to draw to 18-15 down and set his side up for a 10-minute assault on the tourists.

But they were the last points Scotland would score as the Wallabies forwards repelled the Scots and their outside backs forced a ruck penalty for Leali'ifano to get some breathing space with his third three-pointer.

The tourists then defended for their lives as the centre missed two more penalty attempts which could have made it an easier night.

Missing stood-down wingers Adam Ashley-Cooper and Nick Cummins, a patched-up backline received few opportunities with clean ball but fly half Cooper and Folau shone whenever there was a skerrick of an attacking chance.

South African referee Jaco Peyper's whistle dominated the first half as he was quick to find indiscretions at the breakdown.

The Scots took a 6-3 lead and could have pushed ahead an extra three when Cooper conceded a dubious penalty for taking out his cousin, full-back Sean Maitland, from a kick he almost charged down.

But momentum changed when Laidlaw made his only miss of the half.

Leali'ifano almost immediately evened the scores and then Cooper found Folau on his inside and the big full-back fended off Ryan Grant to sprint 25 metres to score his ninth try in 14 Tests.

The pair also combined with Stephen Moore for the play of the match after half-time as the fly half handled twice to put winger Chris Feauai-Sautia over in his run-on debut.

Scotland's best chance came when it almost grabbed the lead at half-time with flanker Johnnie Beattie breaking clear 70 metres out and feeding Maitland, who stepped past Joe Tomane. He then found winger Sean Lamont but Folau was again the man for Australia, running him down in the corner.